I think it would be very useful to explicitly state what the consequences of utility functions being only defined up to an “affine transformation” are in the grandparent post instead of assuming that everyone knows this at a 5-second level. My immediate reaction to the parent post was to look at the wikipedia article for affine transformations without much enlightenment.
Temperature is pretty useless as an analogy, because everyone knows that 2*40 degrees = 80 degrees; you have to think about moving between Celsius and Fahrenheit to actually get something useful out of the analogy. Voltage is even less helpful, because all it depends on is having a fixed reference point (i.e., differences between two voltages are always preserved, even if you change zero points), while distances aren’t preserved in general under affine transformations.
The downvoted post and your response are the most valuable in this entire thread, as they were the only ones that clearly communicated what the actual ramifications of utility functions only being defined up to an affine transformation were.
Ugh. Sorry if this came across as snarky, but the grandparent post came across as “If this young man expresses himself in terms too deep for me,/Why, what a very singularly deep young man/this deep young man must be!”
Except 2*40 degrees isn’t 80 degrees; the operation “2*40 degrees” is simply meaningless in the first place. (I mean, unless that’s a temperature difference of 40 degrees.)
(I mean, OK, you can strictly speaking double a temperature, but in order to do so you need to know what absolute zero is.)
I think it would be very useful to explicitly state what the consequences of utility functions being only defined up to an “affine transformation” are in the grandparent post instead of assuming that everyone knows this at a 5-second level. My immediate reaction to the parent post was to look at the wikipedia article for affine transformations without much enlightenment.
Temperature is pretty useless as an analogy, because everyone knows that 2*40 degrees = 80 degrees; you have to think about moving between Celsius and Fahrenheit to actually get something useful out of the analogy. Voltage is even less helpful, because all it depends on is having a fixed reference point (i.e., differences between two voltages are always preserved, even if you change zero points), while distances aren’t preserved in general under affine transformations.
The downvoted post and your response are the most valuable in this entire thread, as they were the only ones that clearly communicated what the actual ramifications of utility functions only being defined up to an affine transformation were.
Ugh. Sorry if this came across as snarky, but the grandparent post came across as “If this young man expresses himself in terms too deep for me,/Why, what a very singularly deep young man/this deep young man must be!”
Except 2*40 degrees isn’t 80 degrees; the operation “2*40 degrees” is simply meaningless in the first place. (I mean, unless that’s a temperature difference of 40 degrees.)
(I mean, OK, you can strictly speaking double a temperature, but in order to do so you need to know what absolute zero is.)